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arXiv:1011.0033 · Physical Review A

Confinement-induced p -wave resonances from s -wave interactions

Yusuke Nishida, Shina Tan

Published Dec 27, 2010• 39 citations
arXivHTMLPDF

Abstract

We show that a purely $s$-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D $s$-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the $p$-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the $p$-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)] can be interpreted as the $p$-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under $p$-wave resonant scatterers.

DOI
10.1103/physreva.82.062713

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We show that a purely sss-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D sss-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the ppp-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the ppp-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett. 104, 153202 (2010)] can be interpreted as the ppp-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under ppp-wave resonant scatterers.
A dual confinement induced resonance effect first observed numerically in a paper [J. I. Kim, V. S. Melezhik and P. Schmelcher, Phys. Rev. Letters 97 (2006), 193203] predicts the possibility of suppressing the effective two-body interaction in a quasi-one dimensional (1D) cylindrical geometry. Here this low dimensionality effect is analytically modeled by applying a previous formalism to treat low energy quantum scattering processes under tight confinement [J. I. Kim, J. Schmiedmayer and P. Schmelcher, Phys. Rev. A 72 (2005), 042711]. This analytic formalism is improved in order to account non-perturbatively for the three dimensional (3D) scattering phase shift l = 1 for a given spherically symmetric interaction potential between distinguishable colliding particles. The role of the confinement on the scattering properties can then be systematically calculated up to the p-wave.
We observe d-wave confinement-induced resonances (CIRs) of bosonic scattering in tightly confining harmonic waveguides. It is shown that the d-wave CIR emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave CIR is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave CIRs. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a novel possibility for studying strongly correlated atomic systems beyond s-wave physics. PACS numbers: 03.75.Be, 34.10.+x, 34.50.-s
We point out that theories describing s -wave collisions of bosonic atoms confined in one-dimensional (1D) or two-dimensional (2D) geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries.
The two-body scattering is greatly modified in reduced dimensions. With ultracold atoms, low dimensional configurations are routinely accessible thanks to the use of optical lattices which allow confinements sufficiently strong to freeze the motion along chosen directions. With two different atomic species, we use a species-selective optical potential, in the form of a standing wave, to confine only one species in 2D disks and study the scattering between particles existing in different dimensions, i.e., we realize a 2D-3D mix-dimensional configuration , reminiscent of a brane world. We review the scattering theory specific to this configuration and derive an effective scattering length α eff in terms of the free-space scattering length α and the confinement parameters. We detect experimentally the enhancement of inelastic collisions arising at particular values of α and relate these values to the divergences of α eff . Unlike the confinement-induced resonances predicted and observed for identical particles, our mixed-dimensional resonances occur in a series of several resonances, because the relative and centre-of-mass motion are coupled.
Low energy scattering amplitudes for two atoms in one- and two-dimensional atomic waveguides are derived for short range isotropic and resonant interactions in high partial wave channels. Taking into account the finite width of the resonance which was neglected in previous works is shown to have important implications in the properties of the confinement induced resonances. For spin polarized fermions in quasi-1D waveguides, it imposes a strong constraint on the atomic density for achieving the Fermi Tonks Girardeau gas. For a planar waveguide, the characteristics of the 2D induced scattering resonances in p- and d-waves are determined as a function of the 3D scattering parameters and of the waveguide frequency.
We observe and analyze ddd-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the ddd-wave resonance emerges in the quasi-1D regime as an imprint of a 3D ddd-wave shape resonance. A scaling relation for the position of the ddd-wave resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from sss-wave to ddd-wave resonant behavior. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a possibility for studying strongly correlated atomic systems beyond sss-wave physics.